The sum of two numbers is $150$, and their difference is $30$. What are the two numbers?
Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 150}$ ${x-y = 30}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 180 $ $ x = \dfrac{180}{2} $ ${x = 90}$ Now that you know ${x = 90}$ , plug it back into $ {x+y = 150}$ to find $y$ ${(90)}{ + y = 150}$ ${y = 60}$ You can also plug ${x = 90}$ into $ {x-y = 30}$ and get the same answer for $y$ ${(90)}{ - y = 30}$ ${y = 60}$ Therefore, the larger number is $90$, and the smaller number is $60$.